Colligative Properties

Some of the properties of a solution are dependent
primarily on the identity of the solvent and the amount (rather than the
identity) of the solute. These properties are known collectively as
colligative properties.

Vapor Pressure Lowering and Raoult's Law

In solutions that have a non-volatile solute and a
liquid solvent, the presence of the solute alters the behavior of the
solvent. The vapor pressure of a pure solvent is always higher than the
vapor pressure of a solution. We can use kinetic molecular theory to
understand this effect. Vapor pressure is due to the evaporation of a
small amount of the liquid. Remember the discussion on phase changes. If
the liquid is part of a solution, the non-volatile solute molecules act
to disrupt the evaporation process by attracting the solute molecules,
since they have intermolecular forces at least as strong as the liquid
molecules, they impede evaporation. The presence of the solute does not
affect the condensation process, because, since it is non-volatile, it
is not present in the vapor phase.

'My Dog Has Fleas' Analogy

The solvent molecules outnumber the solute, and
they are spread uniformly throughout the solution, so how do they
‘block’ the surface and prevent evaporation? It is a common
misconception to think of the solute as a film on the surface that forms
an impenetrable barrier to prevent vaporization. WRONG. Remember that
substances dissolve because they have favorable intermolecular
attractions with the solvent. Each solute molecule has a sphere of
solute with which it is interacting. The solvent sphere, in turn, has
another layer of solvent molecules with which they are interacting, and
so on, like layers of an onion. Because the non-volatile solute will not
enter the vapor phase, the solvent molecules interacting with the solute
are less likely to vaporize than if the solute were not there.

To understand the effect of a non-volatile solute
on the vapor pressure, imagine that the solute molecules are pet fleas.
I keep my pet fleas in my yard which is surrounded by a chain link
fence. The fleas are energetic and tiny, so the ones inside the yard can
hop through the fence (this is vaporization). The fleas outside the
fence are free to hop back inside (this is condensation) just as easily
as other fleas hop out. After a while, the number of fleas inside the
yard and the number outside the yard settles down and stays fairly
constant, even though individual fleas are moving in and out (this is
the vapor pressure). Suppose I get a pet dog and keep it in the yard
with the fleas. The dog will disrupt the flow of fleas out of the yard,
but not because he blocks up all the holes in the fence. While some of
the fleas, unaware of the dog, continue to hop in and out as before,
some of the fleas are busy interacting with the dog. The dog is too big
to fit through the holes in the chain link fence (he is non-volatile),
so he wanders randomly throughout the yard. Fleas outside the fence are
just as likely to hop inside as before. Fleas inside the fence can still
hop out, but fewer choose to do so because they prefer to pursue a
dog-related lifestyle (these are part of the solvent shell surrounding
the solute particles). Eventually, the number of fleas outside the fence
will drop relative to the pre-dog conditions (the vapor pressure of the
solution is lower than that of the pure solvent). Note that this process
doesn’t depend on the type of dog I have. I could get a pet Chihuahua or
Doberman or a cat or even an elephant. Any pet that fleas like (solute)
that is too large to fit through the fence (non-volatile) will decrease
the number of fleas outside the fence (lower the vapor pressure).

Raoult’s Law

To calculate the extent of the vapor pressure
lowering we can use Raoult’s Law:

where P is the partial pressure of the component A,
X is the mole fraction of component A, and P°
is the partial pressure of component A.

An ideal solution is one that obeys Raoult’s law,
but the behavior of a real solution follows that predicted by Raoult’s
law only approximately. If the intermolecular attractions between the
solute and solvent are very strong, the vapor pressure of the solution
is even lower than what is predicted by Raoult’s Law. The solute
molecules have strong enough attractions to the solvent to prevent
evaporation to a greater degree. If the intermolecular attractions
between solute and solvent are weaker than those of the pure solvent for
itself, the vapor pressure will be lower than that predicted by Raoult’s
Law. The vapor pressure will still be lower than that of the pure
solvent because part of the surface is physically blocked by solute.
However, the lower intermolecular forces allow the solvent molecules to
evaporate more easily than they would if the solute had stronger
attractions.

Vapor pressure lowering is not often observed in a
freshman chemistry lab because it is difficult to accurately measure
small pressure differences unless students have access to expensive
equipment.

Boiling Point Elevation

The boiling point of a pure liquid is lower than
the boiling point of a mixture at any given pressure. The presence of
solute molecules hinders the liquid leaving the mixture, so it takes
higher average kinetic energy and higher temperature. The mechanism of
this effect is similar to that of vapor pressure lowering—the solute
contributes to the attractive force holding the liquid phase together
without taking part in the vaporization.

The extent of the increase in temperature of the
boiling point follows the formula

where ΔTb
is the boiling point increase in degrees Celsius, m is molality of the
solution in mol/kg, Kb is a proportionality constant with
units of °C kg/mol, and i is the
van’t Hoff i-factor, which is does not have units. The boiling point
elevation constant is unique for each solvent. The i-factor is a measure
of the number of particles each solute particle dissociates into when it
dissolves. For non-electrolytes, i = 1. For weak solutions of strong
electrolytes, i is about equal to the number of ions in the formula
unit.

Note that the identity of the solute is not
important, only the amount of solute in the solution matters. The
properties of the solvent determine the value for the boiling
point elevation constant and the boiling temperature of the pure liquid.

The boiling point elevation may be observed
qualitatively by measuring the temperature of salt water that has
reached a rolling boil and comparing this to the normal boiling
temperature of 100 °C. It is not
practical to measure the boiling point elevation quantitatively,
however, because the concentration of the solution increases as the
solvent vaporizes, so it is very difficult to determine the molality.

Freezing Point Depression

The freezing point of a pure liquid is higher than
the freezing point of a mixture. The presence of solute molecules
hinders the formation of the solid phase. We can use kinetic molecular
theory to explain this if we think of the freezing point as being the
same as the melting point, just from a different perspective. When an
ideal mixture freezes, the molecules of one of the components group
together to form a crystal structure held together by intermolecular
forces. A pure crystalline solid forms as the remaining liquid gets more
and more concentrated with the solute impurities. The molecules need
kinetic energy to separate them physically from the mixture, so the
solidification process doesn’t start until the liquid is colder than the
temperature required to freeze the pure liquid. As the liquid freezes,
molecules must move through the solute to join the crystal. At the same
time, some of the individual molecules of pure solid are melting and
mixing with the liquid solution. It is easier for the pure solid to melt
than for the solvent to move through the solution so that it can freeze
(by easier we mean less restricted by attractions with foreign particles). At a temperature that would be low enough to freeze
a pure liquid, the melting process is easier than the freezing process,
so the mixture remains liquid. The mixture has to be cooled lower than
the normal freezing point for the pure crystalline solid to form from
the mixture.

The extent of the decrease in temperature of the
freezing point follows the formula

where ΔTf
is the freezing point decrease in degrees Celsius, m is molality of the
solution in mol/kg, Kf is a proportionality constant with
units of °C kg/mol, and i is the
van’t Hoff i-factor, which is does not have units. The freezing point
depression constant is unique for each solvent. The i-factor is a
measure of the number of particles each solute particle dissociates into
when it dissolves. For non-electrolytes, i = 1. For weak solutions of
strong electrolytes, i is about equal to the number of ions in the
formula unit.

Note that the identity of the solute is not
important, only the amount of solute in the solution matters. The
properties of the solvent determine the value for the boiling
point elevation constant and the boiling temperature of the pure liquid.

Freshman chemistry students usually perform a
freezing point depression experiment to illustrate colligative
properties. The purpose of the experiment is often to determine the
formula weight of an unknown solute, unfortunately. This confuses some
students; the main thrust of colligative properties is that they depend
on the identity of the solvent and the amount of the solute
yet, in this type of experiment, we use the information to find a
formula weight for the solute—it seems contradictory! The explanation
is that the experiment uses the freezing point depression to find the
molality. If you know the mass of the solvent used to make a solution
with a specific molality, you can find the moles of solute. Divide the
mass of the solute by the number of moles to get the formula weight of
the solute.

A real world example of freezing point depression
is the use of antifreeze in a car radiator, salting roads to melt ice,
and using rock salt when you make ice cream.

Concept Check: If used to melt ice, which would do a better job,
sugar (a non-electrolyte), salt, or calcium chloride?

Answer: The calcium chloride would work better. Because the
sugar is a non-electrolyte, it does not break apart into smaller but
more numerous ions when it dissolves. The sodium chloride and calcium
chloride are ionic compounds. These ionize in solution to form two and
three ions per formula unit, respectively. Because calcium chloride
forms more ions, and colligative properties depend on the number of
solute particles, the calcium chloride will result in a larger freezing
point depression.

Additional benefits can be seen if we investigate
cost (sugar is the most expensive, salt is the least expensive), damage
(salt harms concrete and brick), and heat (calcium chloride actually
releases considerable heat when it dissolves as we will see in the unit
about thermochemistry).

Concept Check: Automobile antifreeze is ethylene glycol, C2H6O2.
It is a non-electrolyte. If a radiator contains 40.0% antifreeze and
60.0% water, by mass, what is the freezing point of the solution in the
radiator? The normal freezing point for water is 0.0
°C and Kf is 1.86
°C mol/kg.

Answer: Find the molality of the solution. The mass of the
solvent is 0.0600 kg and the formula weight of the solute is 62.066
g/mol.

Use the freezing point depression formula

Osmosis

Osmosis is the passage of certain molecules through
a membrane. For example, water will flow through a cell membrane.
Membranes are semi-permeable, because they permit molecules that are
small enough to pass while serving as a barrier to other molecules. For
example, animal cells are surrounded by cell membranes which keep the
contents of the cell inside but allow water to flow in and out.

If solutions of differing concentrations are
separated by a semi-permeable membrane, small molecules will flow
through the membrane from the side with the most to the side with the
least until the amounts on both sides of the membrane are equal.
Frequently, water is able to pass through a semi-permeable membrane,
since it is a small molecule, but solute molecules cannot. If this is
the case, water will flow from the side with the lowest concentration
(more water relative to solute) to the side with the highest
concentration (less water relative to solute), diluting it until both
sides are equal.

We can use kinetic molecular theory to explain this
process. If we examine a semi-permeable membrane under magnification, we
see that it is porous. Small molecules can fit inside the pores. Random
molecular motions send small molecules from one side of the membrane to
the other through the pores. Large molecules cannot fit through the
pores, though. Not only do the large molecules stay on one side of the
barrier, they hinder the movement of small molecules through, rather
like they hinder liquid molecules from evaporating from a solution
(remember the dog and fleas analogy). The small molecules can travel
into the side with large solute more readily than
they can travel out of the side with the solute.

The force generated by the net flow of small
molecules through a semi-permeable membrane will support a column of
liquid; much like air pressure supports a column of mercury in a
barometer. We can prevent the flow of small molecules by exerting
pressure against the direction of the flow. The amount of force needed
to equal the force due to the flow of small molecules is called the
osmotic pressure, π.

The osmotic pressure for an ideal solution is
analogous to the ideal gas law

where T is temperature in Kelvin, V is volume, R is
the gas constant and n is the number of moles of solute. This can be
rearranged to

where M is molarity of the solution, since n is
number of moles of solute and V is the volume of the solution.